Directed Transmission Method, A Fully Asynchronous approach to Solve Sparse Linear Systems in Parallel

There are many algorithms to solve large sparse linear systems in parallel; however, most of them acquire synchronization and thus are lack of scalability. In this paper, we propose a new distributed numerical algorithm, called Directed Transmission Method (DTM). DTM is a fully asynchronous, scalable and continuous-time iterative algorithm to solve the arbitrarily-large sparse linear system whose coefficient matrix is symmetric-positive-definite (SPD). DTM is able to be freely running on the heterogeneous parallel computer with arbitrary number of processors, which might be manycore microprocessors, clusters, grids, clouds, and the Internet. We proved that DTM is convergent by making use of the final value theorem of Laplacian Transformation. Numerical experiments show that DTM is efficient.